Introduction to numerical methods

From CFD-Wiki

Fluids could be regarded as substances those on application of external force deform or show very little resistance to deformation. This deformation in the cases of liquid and gases is substantial. Both obey common lows of motion and both for most practical computational purposes can be regarded as continuum. Forces can be considered as body forces, example: forces due to gravity or they can be considered as surface forces example: surface tension.

Based upon their Mach number. This Mach number could be used to determine whether the flow shall be considered as Incompressible flow or Compressible flow for computational purposes. For the flows of Mach number smaller than 0.3, we can safely assume them as incompressible for all computational purposes.

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Control Volume Approach

Conservation laws can be applied to given quantity of fluid. However, it is more convenient to apply them on a small spatial region, called Control volume. For this purposes the geometry under consideration is subdivided into smaller sub-regions. Together they are called mesh or grid. And the approach used is called Control volume approach for solving the flow problem.
The figure 1.1 shows one such computational domain.
Figure 1.1